Find the volume of the pyramid (tetrahedron) with vertices at the points: A(-3,2,1), B(12,-1,0), C(3,1,0) and D(1,1,5). Also find the equation of the height DE and coordinates of the point E. A--E-C 3.

Q: The base of a certain solid is the triangle with vertices at (-6, 3), (3, 3), and the origin.…

A:

Q: the volume of tetrahedron having the vertices (3, -1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A:

Q: A triangular lot XYZ were measured with the following dimensions: XY=150.25m, YZ= 276.45m and ZX=…

A: Topic = Area

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: The given equation of plane is : x+2y+3z=6 x=6-2y-3z                   …(1) Volume of a rectangular…

Q: Find the volume of a napkin ring created by drilling a hole of radius r through the center of a…

A: The volume of a solid, obtained by rotating about the y axis, the region under the curve y = f (x)…

Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed inthe ellipse x2/a2…

A: To find the dimensions of the rectangle of largest perimeter that can be inscribed in the…

Q: Find the volume of the tetrahedron having the given vertices. (4, -2, 1), (3, -1, 4), (1, 1, 1), (0,…

A:

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A:

Q: 3 25 3 3. 6. 6, 2.

A: Solution: The objective is to find the surface area of the right triangular prism

Q: The diagram below shows a right square pyramid with a base that is 6 centimeters (cm) on each side…

A: Volume of pyramid=13Area of basexheight 96=1362 x h h=96 x 36 x 6 h=8 cm

Q: Find the volume of the tetrahedron with the given vertices.(1, 1, 1), (0, 0, 0), (2, 1, −1), (−1, 1,…

A: The vertices of tetrahedron are A(1, 1, 1), O(0, 0, 0), B(2, 1, −1),C (−1, 1, 2) Then,

Q: A storage shed is in the shape of a trapezoidal prism. Each trapezoid represents one of its bases.…

A:

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A:

Q: Find the volume of the Sphere 5 m¸-

A:

Q: Find the dimensions of the right cylinder with largest volume that can be inscribed in a sphere with…

A:

Q: 4 2 8

A: Use the figure for the triangular prism to find the length l, height h and base b. From the figure,…

Q: 2. Calculate the volume of the parallelepiped created by PA, PB and PC, when P (3, - 2, 1), A(5, -…

A: Given that, parallelepiped with edges PA→, PB→ and PC→ Where, P3,-2,1, A5,-6,0, B0,-6,-4 and…

Q: Find the volume of the torus formed by revolving the circle x²+y2=1 about the line x-4. 25.13 cubic…

A: We have to find the volume of torus formed by revolving the circle x2+y2=1 about the line x = 4. To…

Q: Find the volume of the tetrahedron with the given vertices.(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1,…

A: We have given the vertices of tetrahedron; (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1) Since volume…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(5, 3, 5),…

A: Given three vectors, there is a product, called scalar triple product, that gives (the absolute…

Q: Choose the best coordinate system to find the volume of the portion of the solid sphere ps3 that…

A: Using spherical coordinate.

Q: the volume of tetrahedron having the vertices (3,-1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A: Given vertices (3,-1,1), (4,-4,4), (1,1,1), (0,0,1) volume of tetrahedron is equal to 16 of the…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: We have to find the volume of the largest rectangular box in the first octant with three faces in…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(2, 2, 2),…

A:

Q: Find the surface area of the regular pyramid. 2. 1. 9 m

A:

Q: If X = 6 units, Y = 16 units, and Z = 9 units, what is the volume of the right rectangular pyramid…

A: Given that  X = 6 units, Y = 16 units, and Z = 9 units Volume can be found using following formula :…

Q: Find the volume of the torus generated by revolving the circle (x - 2)2 + y2 = 1 about the y-axis.

A: To determine the volume of the torus generated by revolving the circle.

Q: Find the volume of the tetrahedron having the given vertices. (4, -4, 1), (3, -5, 4), (2, 1, 1), (0,…

A: The given vertices are named as follows. P(4, -4, 1), Q(3, -5, 4), R(2, 1, 1) and S( 0, 0, 1).…

Q: Find the volume of the tetrahedron having the given vertices. (5, -5, 1), (3, -4, 4), (1, 1, 1), (0,…

A: We have to find the tetrahedron

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(-2,1,0), Q(2,3,2),…

A:

Q: find the volume of a right triangular prism whose altitude is 3m and a right triangular base whose…

A: Height of the right triangular prism is 3 m. h=3 Legs of right triangular base are 1 m and 2 m.…

Q: Find the volume of the tetrahedron with the given vertices.(0, 0, 0), (0, 2, 0), (3, 0, 0), (1, 1,…

A: The given vertices of a tetrahedron are (0,0,0), (0,2,0), (3,0,0) ,(1,1,4)

Q: Find the volume of the parallelepiped with. adjacent edges PQ, PR, and PS, where P(-2,1,0),…

A: Given- P-2,1,0,Q2,3,2,R1,4,4 and S3,6,1 To Find- The volume of the parallelepiped with the adjacent…

Q: How many square units is the area of the region bounded by the parabolas y = x^2 and y = -x^2 + 4x ?

A:

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(1, 0, 1), Q(-4, 1, 6), R(4,…

A: Given: P1,0,1,Q-4,1,6,R4,1,-1,S0,6,3 To find the vectors representing the adjacent edges:…

Q: Find the volume of the parallelepiped with adjacent sides PQ, PR and PS where P=(0,1, 2), Q=(2, 4,…

A: To find the volume of the parallelpiped with adjacent sides PQ, PR, and PS, where,P=0, 1, 2, Q=2, 4,…

Q: Find the lateral area of a right pentagonal prism with height 13 and baseedges 3.2, 5.8, 6.9, 4.7,…

A: Given that, Height of a right pentagonal prism = 13 And base edges are 3.2, 5.8, 6.9, 4.7 and 9.4

Q: Find the volume of the tetrahedron with the given vertices. (-3, –3, –3) (3, –1, –3), (-3, –1, –3),…

A:

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(3, 4, 3),…

A:

Q: 3 4 3 4

A:

Q: the volume of tetrahedron having the vertices (3, -1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A: Given :  vertices of the tetrahedron are A(3, -1, 1), B(4, -4, 4), C(1,1,1) and D(0,0,1)   To find :…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(3, 0, 1), Q(2, 3,…

A:

Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-2, -1, -3), Q(0, 2,…

A: The given points P-2,-1,-3, Q0,2,0, R-3,-2,-4, S4,-3,-1

Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(3, -4, -1), Q(5, -1,…

A: Given Points are:

Q: Find the volume of the tetrahedron with the given vertices. (4, 0, 0), (0, 2, 0), (0, 0, 1), (4, 2,…

A:

Q: A popcorn container at a movie theater has the shape of a frustum of a pyramid. With dimensions as…

A: Given- To Find- The volume of the above popcorn container. Formula Used- The volume of the square…

Q: Find volume of square revolved around y-axis given following points: (4,5), (4,1), (6,3), (2,3)

A: We need to find the volume of the solid formed when the above square revolves around the y-axis.…

Q: the volume of tetrahedron having the vertices (3, -1, 1), (4, -4, 4), (1, 1, 1), (0, 0, 1) Select…

A: Given vertices (3, −1, 1), (4, −4, 4), (1, 1, 1), (0, 0, 1)

Q: Find the volume of the tetrahedron having the given vertices. (4, -3, 1), (5, -4, 4), (2, 1, 1), (0,…

A:

Q: The diagram below shows a right square pyramid with a base that is 6 centimeters (cm) on each side.…

A: Volume of pyramid